Python access toolbox's parameters after calling an operator
A good rule of thumb is to use auto-complete in the python console, ie type in bpy.ops.mesh.add_lsystem(ctrl-space

&gt;&gt;&gt; bpy.ops.mesh.add_lsystem(
add_lsystem()
bpy.ops.mesh.add_lsystem(nproductions=0, niterations=0, seed=0, start="", radius=0.2, pitch_angle=0.523599, yaw_angle=0.523599, roll_angle=0.523599, tropism=(0, 0, 0), tropismsize=0)


Note: after running manually once it gives the more bloated version with the mods n prods.

&gt;&gt;&gt; bpy.ops.mesh.add_lsystem(
add_lsystem()
bpy.ops.mesh.add_lsystem(nproductions=0, niterations=0, seed=0, start="", radius=0.2, pitch_angle=0.523599, yaw_angle=0.523599, roll_angle=0.523599, tropism=(0, 0, 0), tropismsize=0, prod1="", mod1="", prod2="", mod2="", prod3="", mod3="", prod4="", mod4="", prod5="", mod5="", prod6="", mod6="", prod7="", mod7="", prod8="", mod8="", prod9="", mod9="")


which will give the properties that can be passed to the operator.

For the preset, right click on the preset menu, 



which in my case, for a preset named "Default" gives me the following command in the paste buffer

bpy.ops.script.execute_preset(filepath="/home/batfinger/.config/blender/2.77/scripts/presets/operator/mesh.add_lsystem/default.py", menu_idname="WM_MT_operator_presets")